Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of （generalized） switched Byrnes-Isidori canonical form, which has all switched models in （generalized） Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to （generalized） switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Stability of Delayed Switched Systems With State-Dependent Switching

This paper investigates the stability of switched systems with time-varying delay and all unstable subsystems. According to the stable convex combination, we design a state-dependent switching rule. By employing Wirtinger integral inequality and Leibniz-Newton formula, the stability results of nonlinear delayed switched systems whose nonlinear terms satisfy Lipschitz condition under the designed state-dependent switching rule are established for different assumptions on time delay. Moreover,some new stability results for linear delayed switched systems are also presented. The effectiveness of the proposed results is validated by three typical numerical examples.     

Study on the stability of switched dissipative Hamiltonian systems

The hybrid Hamiltonian system is a kind of important nonlinear hybrid systems. Such a system not only plays an important role in the development of hybrid control theory, but also finds many applications in practical control designs for obtaining better control performances. This paper investigates the stability of switched dissipative Hamiltonian systems under arbitrary switching paths. Under a realistic assumption, it is shown that the Hamiltonian functions of all the subsystems can be used as the multiple-Lyapunov functions for the switched dissipative Hamiltonian system. Based on this and using the dissipative Hamiltonian structural properties, this paper then proves that the P-norm of the state of switched dissipative Hamiltonian system converges to zero with the time increasing, and presents two sufficient conditions for the asymptotical stability under arbitrary switching paths. Utilizing these new results, this paper also obtains two useful corollaries for the asymptotical stability of switched nonlinear time-invariant systems. Finally, two examples are studied by using the new results proposed in this paper, and some numerical simulations are carried out to support our new results.     

Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems

Exponential stability and robust exponential stability relating to switched systems consisting of stable and unstable nonlinear subsystems are considered in this study. At each switching time instant, the impulsive increments which are nonlinear functions of the states are extended from switched linear systems to switched nonlinear systems. Using the average dwell time method and piecewise Lyapunov function approach, when the total active time of unstable subsystems compared to the total active time of stable subsystems is less than a certain proportion, the exponential stability of the switched system is guaranteed. The switching law is designed which includes the average dwell time of the switched system. Switched systems with uncertainties are also studied. Sufficient conditions of the exponential stability and robust exponential stability are provided for switched nonlinear systems. Finally, simulations show the effectiveness of the result.     

具有块三角结构非线性切换系统的二次稳定性

The problem of globally quadratic stability of switched nonlinear systems in block-triangular form under arbitrary switching is addressed. Under the assumption that all block-subsystems are zero input-to-state stable, a sufficient condition for the problem to be solvable is presented. A common Lyapunov function is constructed iteratively by using the Lyapunov functions of block-subsystems.     

Output feedback stabilization of switched stochastic nonlinear systems under arbitrary switchings

This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.     

Design of two-layer switching rule for stabilization of switched linear systems with mismatched switching

A two-layer switching architecture and a two-layer switching rule for stabilization of switched linear control systems are proposed, under which the mismatched switching between switched systems and their candidate hybrid controllers can be allowed. In the low layer, a state-dependent switching rule with a dwell time constraint to exponentially stabilize switched linear systems is given; in the high layer, supervisory conditions on the mismatched switching frequency and the mismatched switching ratio are presented, under which the closed-loop switched system is still exponentially stable in case of the candidate controller switches delay with respect to the subsystems. Different from the traditional switching rule, the two-layer switching architecture and switching rule have robustness, which in some extend permit mismatched switching between switched subsystems and their candidate controllers.     

On the leader-following exponential consensus of discrete-time linear multi-agent systems over jointly connected switching networks

The leader-following asymptotic consensus problem for general discrete-time linear multi-agent systems over jointly connected switching networks was solved about a decade ago. Recently, the leader-following exponential consensus was further established using the so-called Krasovskii–LaSalle theorem for a class of discrete-time linear switched systems. But this method involves some advanced concepts such as the weak zero-state detectability of some limiting system. In this paper, we offer a simpler solution to the leader-following exponential consensus problem for general discrete-time linear multi-agent systems over jointly connected switching networks. After converting the solvability of the problem to the establishment of the exponential stability for a class of discrete-time linear switched systems, we first show that this class of linear switched systems is uniformly completely observable. Then, we further conclude that the uniform complete observability for this class of linear switched systems implies the exponential stability for the same class of linear switched systems, thus leading to the solution of the leader-following exponential consensus problem. Moreover, our approach also gives rise to an explicit characterization of the exponential convergence rate of the leader-following consensus problem.     

Stabilization of switched linear systems with bounded disturbances and unobservable switchings

This paper studies the stabilization problem of switched linear systems with bounded disturbances. It is assumed that the system switches among an infinite set of uniformly controllable linear systems, and that the switching signals are not observable, but the switching duration has a lower bound. It will be shown that by combining on-line adaptive estimation and control in the controller design, a feedback control law can be constructed which makes the switched linear system globally stable.     

H-infinity filtering for discrete-time switched linear systems under arbitrary switching

This paper is concerned with the problem of H-infinity filtering for discrete-time switched linear systems under arbitrary switching laws.New sufficient conditions for the solvability of the problem are given via switched quadratic Lyapunov functions.Based on Finsler’s lemma,two sets of slack variables with special structure are introduced to provide extra degrees of freedom in optimizing the guaranteed H-infinity performance.Compared to the existing methods,the proposed one has better performances and less conservatism.An example is given to illustrate its effectiveness.     

Observability conditions of switched linear singular systems

The observability problem of switched linear singular(SLS) systems is studied in this paper. Based on the observability definition, the unobservable subspaces of given switching laws are investigated under the condition that all subsystems are regular. A necessary condition and a sufficient condition for observability of SLS systems are given. It is shown that the observability and controllability are dual for some special SLS systems with circulatory switching laws. The method developed here is applicable to the observability analysis of normal switched linear systems.     

Robust H-infinity integral sliding mode control for a class of uncertain switched nonlinear systems

This paper develops a new method to deal with the robust H-infinity control problem for a class of uncertain switched nonlinear systems by using integral sliding mode control. A robust H-infinity integral sliding surface is constructed such that the sliding mode is robust stable with a prescribed disturbance attenuation level γ for a class of switching signals with average dwell time. Furthermore, variable structure controllers are designed to maintain the state of switched system on the sliding surface from the initial time. A numerical example is given to illustrate the effectiveness of the proposed method.     

Practical ϕ 0-stability of switched stochastic nonlinear systems and corresponding stochastic perturbation theory

The aim of this paper is to study the practical ф0 -stability in probability (Pф0 SiP) and practical ф0 -stability in pth mean (Pф0 SpM) of switched stochastic nonlinear systems. Sufficient conditions on such practical properties are obtained by using the comparison principle and the cone-valued Lyapunov function methods. Also, based on an extended comparison principle, a perturbation theory of switched stochastic systems is given.     

Adaptive tracking H-infinity control for switched nonlinear systems with unknown control gain sign

This paper addresses the adaptive tracking control scheme for switched nonlinear systems with unknown control gain sign. The approach relaxes the hypothesis that the upper bound of function control gain is known constant and the bounds of external disturbance and approximation errors of neural networks are known. RBF neural networks (NNs) are used to approximate unknown functions and an H-infinity controller is introduced to enhance robustness. The adaptive updating laws and the admissible switching signals have been derived from switched multiple Lyapunov function method. It’s proved that the resulting closed loop system is asymptotically Lyapunov stable such that the output tracking error performance and H-infinity disturbance attenuation level are well obtained. Finally, a simulation example of Forced Duffing systems is given to illustrate the effectiveness of the proposed control scheme and improve significantly the transient performance.     

A Switched Capacitor Harmonic Compensation Part for Switching Supplies

A new approach based on switched capacitor network to harmonic compensation for switching supplies is presented in the paper,The basic principle is discussed.SPICE simulation is applied to analyze the behaviour of the switched capacitor harmonic compensation part.     

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function (SLF) method with Finsler’s Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.     

An output-based distributed observer and its application to the cooperative linear output regulation problem

In this paper, we first extend an existing stability result for a class of linear switched systems. This extended result will relax the existence conditions of the output-based distributed observer for a leader system subject to jointly connected switching communication networks in the literature. As an application of this output-based distributed observer, we solve the cooperative output regulation problem of a linear multi-agent system subject to jointly connected switching communication networks by composing a purely decentralized control law and the output-based distributed observer based on the certainty equivalence principle.     

Asymptotic stability and disturbance attenuation properties for a class of networked control systems

In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H∞ disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such Networked Control System as a discrete-time switched system. Then the NCSs’ stability and performance problems can be reduced to the corresponding problems for switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based on recent progress in the discrete-time switched systems and piecewise Lyapunov functions.     

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.     

Stability and Stabilization of Block-cascading Switched Linear Systems

The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is (QLFs) is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.